Modeling Reliability for Exponential Distribution Using Maximum Likelihood Method (Case study: A.T.M in Sudan)

Ismaeel Ahmed Mohamed Ahmed, Ahmed Mohamed Abdallah Hamdi, Afra Hashim Abdelateef

1. Currant PhD Student, University of Sudan for Science & Technology, Faculty of Science, Department of Statistics.
2. Associate Professor, University of Sudan for Science & Technology, Faculty of Science, Department of Statistics.
3. Assistant Professor, University of Sudan for Science & Technology, Faculty of Science, Department of Statistics.

Abstract: The exponential distribution is the most commonly used life distribution in applied reliability analysis. The reason for this is its mathematical simplicity and that it leads to realistic lifetime models for certain types of item. The aim of this study is to apply lifetime models on the failure time of the automatic teller machine (ATM) in Sudan and estimate the reliability of the machines, in order to compare between machines, failure’s data has been taken from Central Bank of Sudan, which is, type of machine, type of failure, Downtime, Uptime and outage duration in Hrs. during the period of time (1/1/2017-30/6/2017). The comparison between five machines selected randomly out of 28 machines have done. Through the lifetime models estimation (failure distribution, reliability, hazard rate, and mean time to failure (MTTF)), using maximum likelihood estimators in estimate the parameters and reliability of exponential distribution. The comparison is executed through reliability values; from analysis results it is clear that, the failure time of all machines follow exponential distribution with one-parameter, according to the Kolmogorov-Smirnov test and Chi-Squared test for goodness of fit result. The machines no (B5 and B35) have high reliability compered by other machines. When we predict the reliability according to the time we found that the reliability decrease and hazard rate increase and there is relationship between MTTF and reliability.

Keywords: Reliability, Failure rate, Hazard rate, Exponential Distribution, Maximum likelihood, Kolmogorov-Smirnov test, Chi-Squared test.

Pages: 192 – 209 | Full PDF Paper